The two players are White and Black. We will show white pieces
as capital letters (KQBNRP) and black pieces as small letters
(kqbnrp). White moves first.

The pieces start on the board like this:

kqbnr
ppppp
.....
.....
PPPPP
RNBQK

The pieces move like this:

The King can move one space N, S, E, W, NE, NW, SE or SW.

.....
xx...
Kx...
xx...
.....
.....

The Queen can move as far as she wants N, S, E, W,
NE, NW, SE or SW, as long as no piece is in the way.

x.x..
xx...
QxxB.
xx...
x.x..
x..x.

The Rook can move as far as it wants N, S, E or W, as long as no
piece is in the way.

x....
x....
Rxxxx
x....
B....
.....

The Bishop can move as far as he wants NE,SE,NW or SW, as long
as no piece is in the way.

..x..
.x...
B....
.x...
..R..
.....

The Knight moves two spaces N,S,E or W, then one space
perpendicular to its previous move. It can jump over pieces in the
way.

.x...
..x..
NB...
PPx..
.x...
.....

The White Pawn moves one space N. The Black Pawn moves one
space S. Pawns are blocked by pieces in their way.
A Pawn reaching the far end of the board becomes a Queen.

.....
.....
p....
x....
.....
.....

Except for Pawns, a piece captures by moving onto an opposing
piece. White pawns capture only by moving onto a piece NW or NE;
Black pawns SW or SE.

.....
.....
p....
.x...
.....
.....

Victory conditions:

The first player to capture the opponent's King wins.

A game lasting more than 40 moves (by each side) is a draw.

If a player has no legal move, the game is a
draw. Note that in
mini-chess there is no rule against "moving into check": allowing
your King to be captured is a legal move. (Is a
draw by no legal move even possible under these conditions?)

If you have played chess before, this game is easy to understand.
The changes from normal chess are: